Blanchet, J., Wiesel, J., Zhang, E., & Zhang, Z. (2024). Empirical martingale projections via the adapted Wasserstein distance. ArXiv. /abs/2401.12197

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Abstract

Given a collection of multidimensional pairs , we study the problem of projecting the associated suitably smoothed empirical measure onto the space of martingale couplings (i.e. distributions satisfying ) using the adapted Wasserstein distance. We call the resulting distance the smoothed empirical martingale projection distance (SE-MPD), for which we obtain an explicit characterization. We also show that the space of martingale couplings remains invariant under the smoothing operation. We study the asymptotic limit of the SE-MPD, which converges at a parametric rate as the sample size increases if the pairs are either i.i.d. or satisfy appropriate mixing assumptions. Additional finite-sample results are also investigated. Using these results, we introduce a novel consistent martingale coupling hypothesis test, which we apply to test the existence of arbitrage opportunities in recently introduced neural network-based generative models for asset pricing calibration.

Authors
Jose Blanchet, Johannes Wiesel, Erica Zhang, Zhenyuan Zhang
Publication date
2024/1/22
Journal
arXiv preprint arXiv:2401.12197